High-resolution optical spectrometers (also known as coherent optical spectral analyzers) are used to observe spectral features of an unknown signal. Some high-resolution optical spectrometers implement a heterodyne architecture, based upon principles of coherent optical spectral analysis, to achieve very fine measurement resolution. In accordance with this heterodyne architecture, current high-resolution spectrometers utilize a 2×2 optical coupler to combine the unknown signal with a local oscillator signal generated by a local oscillator that is intentionally set to oscillate at a known frequency or to sweep across a range of frequencies. The two outputs of the coupler are detected through a nonlinear detector, such as a photodiode, and the resulting electrical signals subtracted from one another to produce the desired heterodyne signal. From this, the spectral features of the unknown signal can be obtained.
One of the principle uses of a high-resolution optical spectrometer is to map out the spectral amplitude of the unknown signal as a function of wavelength. To perform such a measurement, the local oscillator signal is swept across different wavelengths, while the heterodyne signal due to mixing with the unknown signal is acquired. Unfortunately, the current receiver architecture, which is based on a 2×2 optical coupler, is unable to measure the precise phase of the heterodyne signal. Since the phase of the heterodyne signal varies throughout the scan, as well as from scan to scan, amplitude uncertainty is introduced into the spectral measurement. This amplitude uncertainty is especially evident when intermediate frequency (IF) receivers with lowpass filters are employed. Furthermore, the inability to observe the phase of the heterodyne signal also results in the receiver being equally sensitive to both positive and negative heterodyne beat frequencies. Therefore, any attempt to reduce phase uncertainty by using a bandpass receiver will result in the formation of spectral images that limit the ultimate resolution of the device.
The problem with measuring the phase of the heterodyne signal stems from the basic phase ambiguity of a sinusoidal function. Typically, the heterodyne signal as described above will have the general form:H(t)=V(t) cos (2πΔft+φ(t))  (1)as shown in Equation 1, where Δf represents a frequency difference between the local oscillator and unknown signals, and φ(t) represents the relative phase of the heterodyne beat signal. A single measurement of H(t) is unable to resolve V(t), the desired heterodyne amplitude, since there are two unknowns (V(t) and φ(t)). Even if V(t) is known or assumed constant in time it is impossible to compute with certainty the phase argument (2πΔft+φ(t)), simply because the arccosine function is not single-valued. Therefore, from a measurement of H(t), it is not possible to know with certainty the relative phase φ(t), nor whether the frequency difference Δf is positive or negative. Furthermore, variations in the amplitude of the heterodyne signal V(t) make determination of the phase argument even more problematic. Ultimately, two independent and simultaneous measurements of H(t) are needed to obtain the two unknowns V(t) and φ(t).
The problem is solved if the heterodyne signal H(t) can be represented as a vector, rather than scalar, quantity. If H(t) is of the form:H(t)=V(t)ei(2πΔft+φ(t))  (2)as shown in Equation 2, then the phase argument (2πΔft+φ(t)) can be computed, without ambiguity, as shown in Equation 3:
                              ∠H          ⁡                      (            t            )                          =                  arctan          ⁡                      (                                          Im                ⁢                                  {                                      H                    ⁡                                          (                      t                      )                                                        }                                                            Re                ⁢                                  {                                      H                    ⁡                                          (                      t                      )                                                        }                                                      )                                              (        3        )            The measurement of the Real and Imaginary components of H(t) constitute the needed dual simultaneous measurement of H(t). The unambiguous nature of this phase computation can easily be understood by drawing H(t) as a vector in the complex plane. There are three main benefits to the vector representation of H(t), over the scalar. Firstly, it becomes completely clear whether the heterodyne frequency Δf is positive or negative. Secondly, the relative phase φ(t) can be determined without ambiguity. Finally, the phase measurement is now completely decoupled from variations in the heterodyne amplitude V(t)—and conversely, measurements of V(t) are insensitive to variations in the phase angle of the heterodyne signal. Herein, any system that generates or operates on a vector heterodyne signal, which in turn may be resolved into an orthogonal basis, will be known as a “phase-diverse” system. With regard to coherent optical spectral analysis, the use of phase-diverse techniques translates directly to spectral image elimination and improved amplitude accuracy.
The issue of phase-diversity has been addressed in the field of coherent optical communications. The use of phase-diverse receivers in coherent communication systems has enabled a number of advances, such as eliminating crosstalk effects from adjacent data channels. However, while phase-diverse receiver techniques have found some application in coherent communications, little has been carried over to the realm of optical spectral analysis. Since optical spectral analysis is focused on measurements in the frequency-domain, rather than time-domain, the receiver requirements are often very different from those in time-domain communications applications.